SECOND GENERATION MODELS
3.1 An Example of Second-Generation Model
In his expository work, Obstfeld (1994) states that speculative anticipations hinge on conjectured government responses, which depend, in turn, on how price changes that are themselves kindled by expectations that affect the government’s
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economic and political positions. He concludes that this circular dynamic implies a potential for crises that need not have occurred, but that do occur since market participants anticipate them to. Below, his model about the role of nominal interest rates is presented in detail.
Figure 2: The Circular Dynamic Potential for Currency Crises
3.1.1 Assumptions
In this set up, the world lasts for two periods, denoted 1 and 2. We will consider the position of a government that issues a domestic currency unit (lira in this set up) but also involves in foreign currency (the mark) market. The government enters period 1 with obligations to pay claimants the nonnegative amounts 0D lira in 1 period 1 and 0D lira in period 2. Likewise, in period 1 the government receives 2 payments of 0 f marks in period 1 and 1 0 f marks in period 2. The real government 2
Price changes
Speculative anticipation Expectations that affect
the government’s economic and political
positions
Conjectured government response
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consumption in the two periods, g1andg2, are given exogenously. Lastly, the government can levy taxes on output at rate τ to balance its budget, but only in period 2.
The assumptions of purchasing power parity and E=Pare employed. In period 1, the lira/mark exchange rate is fixed atE1, however, in period 2 the rate may be changed toE2. The letter i denotes the nominal interest rate on loans made in period 1 and repaid in period 2. The new lira obligations due in period 2 incurred by the government in period 1 are denoted by1D2. Then the period 1 constraint is:
period 1, M1. Thus, the implied period 2 constraint is:
[
1 2 0 2]
2 2 2 2 15 New lira obligations due in period 2 = (1+interest rate)*(lira debt service + government consumption expenditure + acquisition of new mark assets – mark receipts that accrue in period 1)
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Under the capital mobility and uncovered interest-rate parity assumptions, perfect-foresight equilibrium requires the ex-post equality of lira and mark asset returns, measured in lira, intertemporal budget constraint which is expressed in lira:
i
where real output is assumed to be constant.
Subsequently, the government is concerned about the distorting effects of (ex-post) inflation and the tax rate. Due to the fact that these variables are zero in period 1 by assumption, the quadratic loss function the government minimizes can be written as:
21 prices) between periods 1 and 2:
2
We can combine Equations (14) and (15) in order to clarify the fiscal role of the depreciation rateε. This yields:
2
the period 1 price level of the lira government debt payment promised on date t for date s>t.
Equation (21) states that in the second period, the revenues of the inflation levy plus conventional taxes must be sufficient to repay the government’s net debt and pay for current spending.
22 3.1.2 The Sequels of the Model
In period 2, the government chooses εand τ to minimize its quadratic loss function subject to Equation (21). Momentously, all variables in (21) are predetermined exceptε andτ . On the other side, the private sector has rational expectations regarding the objectives of the government. Besides, the forecast of lira depreciation incorporated in the nominal interest rate i is based on the assumption that the government will act in this way.
τ
If we write the Lagrangian and find the first order conditions:
[
1 2 0 2 1 2 0 2 2 1 2 0 2]
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equation above shows how the government’s preferred depreciation rate is influenced by the market interest rate effective in period 1 and by the currency composition government chooses for its debt.
Figure 3: The Set of Equilibrium in Period 1
Source: Obstfeld (1994)
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On the vertical axis of Figure 3, we have the depreciation reaction function of the government showing the depreciation rate εit adopts in period 2 when faced with a lira interest rate of i . It is assumed that the reaction function is positively sloped, which reflects, intuitively, that the possibility that a higher nominal 1 interest rate makes greater currency depreciation optimal by raising the inflation tax base in period 2. At the same time, we have another upward-sloping curve, the interest parity curve, demonstrating the expected rate of depreciation consistent with the lira interest rate prevailing in period 1. The derivation of the interest parity curve goes as
follows: if we combine Equations (16) and (20) it follows that
In a perfect-foresight equilibrium, given market expectations, the depreciation rate which government finds optimal should be equal to the depreciation rate the market expects. Hence, intersection of the interest parity curve and the government reaction function determines the possible equilibria of currency depreciation and nominal interest rates. In Figure 2, there are two equilibria6. Clearly, the government’s loss is lower in the low-depreciation equilibrium
(
i1,ε1)
, but it is not guaranteed that the bond market coordinates on low lira interest rate. Here the government confronts with a dynamic inconsistency problem: it cannot make credible promises regarding not validating the expectations if the bond market agrees on the high-inflation equilibrium’s interest rate.
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Now let us consider the implications of the analysis above for a fixed exchange rate regime. A government always can relinquish a currency peg if economic conditions allow a realignment. Assume, nevertheless, that the government faces a cost c7of realigning. In this case the loss function is:
cZ L= 2 + 2+
2 2
1τ θε
{
Z =1↔ε ≠0,Z =0↔ε =0}
. (23)If the superfluous loss of a fixed exchange rate regime is greater thanc, the government will find it optimal to devalue.
Suppose the market expects the currency to be devalued at the rate ε2and sets the nominal interest rate at the corresponding level i2 as shown in Figure 3. Then the government will be induced to exercise the anticipated devaluation regardless of the realignment costc. This is an example of a self-fulfilling speculative attack: there exists an equilibrium in which the exchange parity can survive, however, the government is led to change the parity since private expectations make it too costly not to.
Obstfeld (1994) asserts that this model captures aspects of the Italian crisis in September 1992, when the government was forced to hinge heavily on Bank of Italy in order to finance its high cash-flow requirements. Besides, the model applies to other situations such as Britain’s in the 1950s and 1960s, when the authorities strived to prevent the collapse of the value of the pound against a large and increasing public debt.
7 This may be a cost that could reflect political embarrassment and credibility loss.
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3.2 The Second-Generation Models Examining the Interactions Among